| Texto completo | |
| Autor(es): |
Barreto, Alexandre Paiva
;
Fontenele, Francisco
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | REVISTA MATEMATICA IBEROAMERICANA; v. 39, n. 4, p. 6-pg., 2023-01-01. |
| Resumo | |
In this paper, we prove that if Mn, n > 3, is a complete Riemannian manifold with negative Ricci curvature and f : Mn symbolscript Rn+1 is an isometric immer-sion such that Rn+1\f (M) is an open set that contains balls of arbitrarily large radius, then infM IAI = 0, where IAI is the norm of the second fundamental form of the immersion. In particular, an n-dimensional complete Riemannian manifold with negative Ricci curvature bounded away from zero cannot be properly isometrically immersed in a half-space of Rn+1. This gives a partial answer to a question raised by Reilly and Yau. (AU) | |
| Processo FAPESP: | 19/20854-0 - Superfícies de Weingarten em R^3 e hipersuperfícies completas com curvatura de Ricci negativa em R^{n+1} |
| Beneficiário: | Alexandre Paiva Barreto |
| Modalidade de apoio: | Auxílio à Pesquisa - Pesquisador Visitante - Brasil |
| Processo FAPESP: | 18/03721-4 - Superfícies de Weingarten, Self-Shrinkers e Superfícies Hiperbólicas |
| Beneficiário: | Alexandre Paiva Barreto |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |